Question 5.5: Using the Term Structure to Compute Present Values Compute t...
Using the Term Structure to Compute Present Values
Compute the present value of a risk-free five-year annuity of $1000 per year, given the yield curve for November 2008 in Figure 5.3.
Plan
The timeline of the cash flows of the annuity is:
We can use the table next to the yield curve to identify the interest rate corresponding to each length of time: 1, 2, 3, 4, and 5 years. With the cash flows and those interest rates, we can compute the PV.
Execute
From Figure 5.3, we see that the interest rates are: 0.91%, 0.98%, 1.26%, 1.69%, and 2.01%, for terms of 1, 2, 3, 4, and 5 years, respectively.
To compute the present value, we discount each cash flow by the corresponding interest rate:
Evaluate
The yield curve tells us the market interest rate per year for each different maturity. In order to correctly calculate the PV of cash flows from five different maturities, we need to use the five different interest rates corresponding to those maturities. Note that we cannot use the annuity formula here because the discount rates differ for each cash flow.
